Sinai University Faculty of Engineering Science Department of Basic Science

1. Sinai University Faculty of Engineering Science Department of Basic Science W1

2. Course namePhysics II- BSM121 Text books 1-Physics for scientists and engineers, Jewett, and Serway 7e 2- Fundamental of physics, Haliday et al, 7e 3-Lecture notes 4- Internet sites Edited by: Prof Ahmed Mohamed El-lawindy E.M: ellawindy@su.edu.eg W1

3. Chapter 23 Electric Fields 23.1 Properties of Electric Charges 23.2 Charging Objects By Induction 23.3 Coulomb’s Law 23.4 The Electric Field 23.5 Electric Field of a Continuous Charge Distribution 23.6 Electric Field Lines 23.7 Motion of Charged Particles in a Uniform Electric Field W1

4. Objectives 1- Determine the Properties of Electric Charges. 2- Define and discuss the Coulomb’s Law. 3- Define the Electric Field 4- Apply the concept of electric field to many point charges. 5- Deriving the electric field due to an arbitrary charge distribution, 6- Illustrate the concept of Electric Field Lines 7- Demonstrate the Motion of Charged Particles in a Uniform Electric Field 8- Solve problems related to the electric charges. W1

5. Electricity and Magnetism, Some History • Many applications • Macroscopic and microscopic • Chinese • Documents suggest that magnetism was observed as early as 2000 BC • Greeks • Electrical and magnetic phenomena as early as 700 BC • Experiments with amber and magnetite • 1600 • William Gilbert showed electrification effects were not confined to just amber • The electrification effects were a general phenomena • 1785 • Charles Coulomb confirmed inverse square law form for electric forces W1

6. Electricity and Magnetism, Some History, 2 • 1819 • Hans Oersted found a compass needle deflected when near a wire carrying an electric current • 1831 • Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire • 1873 • James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism • Unified electricity and magnetism • 1888 • Heinrich Hertz verified Maxwell’s predictions • He produced electromagnetic waves W1

7. 23.1 Properties of Electric Charges Experiments 1-After running a comb through your hair on a dry day you will find that the comb attracts bits of paper. 2-Certain materials are rubbed together, such as glass rubbed with silk or rubber with fur, same effect will appear. 3-Another simple experiment is to rub an inflated balloon with wool. The balloon then adheres to a wall, often for hours.

8. Results When materials behave in this way, they are said to be electrified, or to have become electrically charged. Example: Electrify your body :

9. Electric Charges • There are two kinds of electric charges • Called positive and negative • Negative charges are the type possessed by electrons • Positive charges are the type possessed by protons • Charges of the same sign repel one another • charges with opposite signs attract one another W1

10. More About Electric Charges 1-Electric charge is always conserved in an isolated system • For example, charge is not created in the process of rubbing two objects together • The electrification is due to a transfer of charge from one object to another W1

11. Quantization of Electric Charges 2-The electric charge, q, is said to be quantized • q is the standard symbol used for charge as a variable • Electric charge exists as discrete packets, q = Ne • N is an integer • e is the fundamental unit of charge • |e| = 1.6 x 10-19 C • Electron: q = -e • Proton: q = +e W1

12. Conductors • Electrical conductors are materials in which some of the electrons are free electrons • Free electrons are not bound to the atoms • These electrons can move relatively freely through the material • Examples of good conductors include copper, aluminum and silver • When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material W1

13. Insulators • Electrical insulators are materials in which all of the electrons are bound to atoms • These electrons can not move relatively freely through the material • Examples of good insulators include glass, rubber and wood • When a good insulator is charged in a small region, the charge is unable to move to other regions of the material W1

14. Semiconductors • The electrical properties of semiconductors are somewhere between those of insulators and conductors • Examples of semiconductor materials include silicon and germanium W1

15. -8+8 -4+8 23.2 Charging Objects By Induction • Charging by induction requires no contact with the object inducing the charge • Assume we start with a neutral metallic sphere (The sphere has the same number of positive and negative charges) Procedure of the experiment W1

16. Charging by induction

17. Charge Rearrangement in Insulators • A process similar to induction can take place in insulators • The charges within the molecules of the material are rearranged W1

18. 23.3 Coulomb’s Law • Charles Coulomb measured the magnitudes of electric forces between two small charged spheres • He found the force depended on the charges and the distance between them W1

19. Q Q Q/2 Q/2 Q/2 Q/4 Q/4 Q/4 Q/8 Q/8 Q/8 Q/16 Q/16 23.3 Coulomb’s Law t=kq=FxR=FR F aq

20. Coulomb’s experiment Results The electric force between two stationary charged particles • The term point charge refers to a particle of zero size that carries an electric charge • The electrical behavior of electrons and protons is well described by modeling them as point charges

21. Coulomb’s Law, Equation • Mathematically, • The SI unit of charge is the coulomb (C) • ke is called the Coulomb constant • ke = 1/(4πeo)= 8.9876 x 109 N.m2/C2 • eois the permittivity of free space • eo= 8.8542 x 10-12 C2 / N.m2 W1

22. Coulomb's Law, Notes • Remember the charges need to be in coulombs • e is the smallest unit of charge • except quarks • e = 1.6 x 10-19 C • So 1 C needs 6.24 x 1018 electrons or protons • Typical charges can be in the µC range • Remember that force is a vector quantity W1

23. Particle Summary W1

24. Vector Nature of Electric Forces • In vector form, • is a unit vector directed from q1 to q2 • The like charges produce a repulsive force between them • Electrical forces obey Newton’s Third Law • The force on q1 is equal in magnitude and opposite in direction to the force on q2 PLAY ACTIVE FIGURE W1

25. Vector Nature of Electrical Forces, 3 • Two point charges are separated by a distance r • The unlike charges produce an attractive force between them • With unlike signs for the charges, the product q1q2 is negative and the force is attractive PLAY ACTIVE FIGURE W1

26. Superposition Principle, Example • The force exerted by q1 on q3 is • The force exerted by q2 on q3 is • The resultant force exerted on q3 is the vector sum of and F3= + W1

27. Zero Resultant Force, Example • Where is the resultant force equal to zero? • The magnitudes of the individual forces will be equal • Directions will be opposite • Will result in a quadratic • Choose the root that gives the forces in opposite directions W1

28. Electrical Force with Other Forces, Example • The spheres are in equilibrium • Since they are separated, they exert a repulsive force on each other • Charges are like charges • Proceed as usual with equilibrium problems, noting one force is an electrical force • Solve for |q| • You cannot determine the sign of q, only that they both have same sign W1

29. 23.4 The Electric Field Introduction • The electric force is a field force • Field forces can act through space • The effect is produced even with no physical contact between objects W1

30. Electric Field – Definition • An electric field is said to exist in the region of space around a charged object • This charged object is the source charge • When another charged object, the test charge, enters this electric field, an electric force acts on it W1

31. Electric Field – Definition, cont • The electric field is defined as the electric force on the test charge per unit charge • The electric field vector,, at a point in space is defined as the electric force acting on a positive test charge, qo placed at that point divided by the test charge: W1

32. Electric Field, Notes • is the field produced by some charge or charge distribution, separate from the test charge • The existence of an electric field is a property of the source charge • The presence of the test charge is not necessary for the field to exist • The test charge serves as a detector of the field W1

33. Electric Field Notes, Final • The direction of is that of the force on a positive test charge • The SI units of are N/C • We can also say that an electric field exists at a point if a test charge at that point experiences an electric force E,F W1

34. Relationship Between F and E • This is valid for a point charge only For larger objects, the field may vary over the size of the object • If q is positive, the force and the field are in the same direction • If q is negative, the force and the field are in opposite directions W1

35. Electric Field, Vector Form • Remember Coulomb’s law, between the source and test charges, can be expressed as • Then, the electric field will be W1

36. More About Electric Field Direction • a) q is positive, the force is directed away from q • b) The direction of the field is also away from the positive source charge • c) q is negative, the force is directed toward q • d) The field is also toward the negative source charge PLAY ACTIVE FIGURE W1

37. Superposition with Electric Fields • At any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges W1

38. Superposition Example • Find the electric field due to q1, • Find the electric field due to q2, • Remember, the fields add as vectors • The direction of the individual fields is the direction of the force on a positive test charge W1

39. Electric Field – Continuous Charge Distribution • The distances between charges in a group of charges may be much smaller than the distance between the group and a point of interest • In this situation, the system of charges can be modeled as continuous • The system of closely spaced charges is equivalent to a total charge that is continuously distributed along some line, over some surface, or throughout some volume W1

40. 23.5 Electric Field – Continuous Charge Distribution, cont • Procedure: • Divide the charge distribution into small elements, each of which contains Δq • Calculate the electric field due to one of these elements at point P • Evaluate the total field by summing the contributions of all the charge elements W1

41. Charge Densities • Volume charge density: • when a charge is distributed evenly throughout a volume • ρ≡Q / V with units C/m3 • Surface charge density: • when a charge is distributed evenly over a surface area • σ≡Q / A with units C/m2 • Linear charge density: • when a charge is distributed along a line • λ≡Q / ℓwith units C/m W1

42. Amount of Charge in a Small Volume, Area, and Length • If the charge is nonuniformly distributed over a volume, surface, or line, the amount of charge, dq, is given by • For the volume: dq = ρdV • For the surface: dq = σdA • For the length element: dq = λdℓ W1

43. Problem-Solving Strategy • Conceptualize • Establish a mental representation of the problem • Image the electric field produced by the charges or charge distribution • Categorize • Individual charge? • Group of individual charges? • Continuous distribution of charges? W1

44. Problem-Solving Strategy, cont • Analyze • Units: when using the Coulomb constant, ke, the charges must be in C and the distances in m • Analyzing a group of individual charges: • Use the superposition principle, find the fields due to the individual charges at the point of interest and then add them as vectors to find the resultant field • Be careful with the manipulation of vector quantities • Analyzing a continuous charge distribution: • The vector sums for evaluating the total electric field at some point must be replaced with vector integrals • Divide the charge distribution into infinitesimal pieces, calculate the vector sum by integrating over the entire charge distribution W1

45. Problem Solving Hints, final • Analyze, cont. • Symmetry: • Take advantage of any symmetry to simplify calculations • Finalize • Check to see if the electric field expression is consistent with your mental representation • Check to see if the solution reflects any symmetry present • Image varying parameters to see if the mathematical result changes in a reasonable way W1

46. Example – Charged Disk • The ring has a radius R and a uniform charge density σ • Choose dq as a ring of radius r • The ring has a surface area 2πrdr W1

47. 23.6 Electric Field Lines • Field lines give us a means of representing the electric field pictorially • The electric field vector is tangent to the electric field line at each point • The line has a direction that is the same as that of the electric field vector • The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region W1

48. Electric Field Lines, General • The density of lines through surface A is greater than through surface B • The magnitude of the electric field is greater on surface A than B • The lines at different locations point in different directions • This indicates the field is nonuniform W1

49. Electric Field Lines, Positive Point Charge • The field lines radiate outward in all directions • In three dimensions, the distribution is spherical • The lines are directed away from the source charge • A positive test charge would be repelled away from the positive source charge W1

50. Electric Field Lines, Negative Point Charge • The field lines radiate inward in all directions • The lines are directed toward the source charge • A positive test charge would be attracted toward the negative source charge W1